Stable harmonic 2-spheres in symmetric spaces

Burstall, F.; Rawnsley, J.; Salamon, S.

doi:10.1090/S0273-0979-1987-15516-9

Stable harmonic 2-spheres in symmetric spaces
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by F. Burstall, J. Rawnsley and S. Salamon PDF

Bull. Amer. Math. Soc. 16 (1987), 274-278

References

James Eells Jr. and J. H. Sampson, Harmonic mappings of Riemannian manifolds, Amer. J. Math. 86 (1964), 109–160. MR 164306, DOI 10.2307/2373037
Norio Ejiri, The index of minimal immersions of $S^{2}$ into $S^{2n}$, Math. Z. 184 (1983), no. 1, 127–132. MR 711733, DOI 10.1007/BF01162011
William B. Gordon, Convex functions and harmonic maps, Proc. Amer. Math. Soc. 33 (1972), 433–437. MR 291987, DOI 10.1090/S0002-9939-1972-0291987-1
A. Grothendieck, Sur la classification des fibrés holomorphes sur la sphère de Riemann, Amer. J. Math. 79 (1957), 121–138 (French). MR 87176, DOI 10.2307/2372388
Ralph Howard and S. Walter Wei, Nonexistence of stable harmonic maps to and from certain homogeneous spaces and submanifolds of Euclidean space, Trans. Amer. Math. Soc. 294 (1986), no. 1, 319–331. MR 819950, DOI 10.1090/S0002-9947-1986-0819950-4
J.-L. Koszul and B. Malgrange, Sur certaines structures fibrées complexes, Arch. Math. (Basel) 9 (1958), 102–109 (French). MR 131882, DOI 10.1007/BF02287068
Pui Fai Leung, On the stability of harmonic maps, Harmonic maps (New Orleans, La., 1980) Lecture Notes in Math., vol. 949, Springer, Berlin-New York, 1982, pp. 122–129. MR 673586
André Lichnerowicz, Applications harmoniques et variétés kähleriennes, Symposia Mathematica, Vol. III (INDAM, Rome, 1968/69) Academic Press, London, 1968/1969, pp. 341–402 (French). MR 0262993
John Douglas Moore, Compact Riemannian manifolds with positive curvature operators, Bull. Amer. Math. Soc. (N.S.) 14 (1986), no. 2, 279–282. MR 828826, DOI 10.1090/S0273-0979-1986-15440-6
Yoshihiro Ohnita, Stability of harmonic maps and standard minimal immersions, Tohoku Math. J. (2) 38 (1986), no. 2, 259–267. MR 843811, DOI 10.2748/tmj/1178228492
J. Sacks and K. Uhlenbeck, The existence of minimal immersions of $2$-spheres, Ann. of Math. (2) 113 (1981), no. 1, 1–24. MR 604040, DOI 10.2307/1971131
Yum Tong Siu, Some remarks on the complex-analyticity of harmonic maps, Southeast Asian Bull. Math. 3 (1979), no. 2, 240–253. MR 564815
Yum Tong Siu and Shing Tung Yau, Compact Kähler manifolds of positive bisectional curvature, Invent. Math. 59 (1980), no. 2, 189–204. MR 577360, DOI 10.1007/BF01390043
R. T. Smith, The second variation formula for harmonic mappings, Proc. Amer. Math. Soc. 47 (1975), 229–236. MR 375386, DOI 10.1090/S0002-9939-1975-0375386-2
A. V. Tyrin, Critical points of the multidimensional Dirichlet functional, Mat. Sb. (N.S.) 124(166) (1984), no. 1, 146–158 (Russian). MR 743062
Joseph A. Wolf, Complex homogeneous contact manifolds and quaternionic symmetric spaces, J. Math. Mech. 14 (1965), 1033–1047. MR 0185554
W. J. Zakrzewski, Classical solutions of two-dimensional Grassmannian models, J. Geom. Phys. 1 (1984), no. 2, 39–63. MR 794979, DOI 10.1016/0393-0440(84)90003-2